Back to your issue. YES, a lot of work with chisels and rasps. I’ve been building for over 25 years, and in my opinion, this is the toughest parts of the build. Mostly because you are inletting 2 directions at once, forward and down.
It will help to get the contour of the butt first, then mark and chisel till it’s in place.
Super sharp tools are a must!